1. The Thomas Edison program is a good program, they are very flexible and work with you to finish classes, something that will be very important during your time in the Navy. Completing college classes while enduring sea duty can be a very difficult task unless you are extremely focused on it (and it certainly won't be allowed by your command until you have qualified your senior in rate watchstation, which can take up to 18 months). I am enrolled in this program myself and recommend it if you are going to pursue a degree while on sea duty. As charlierock said, RPI has a good program, but you have to be on shore duty at the Ballston Spa Prototype to use it. Similar programs are available to staff stationed in Charleston, SC (This would require additional service).
2. As far as nukes getting picked up for officer programs goes, i don't know how the surface numbers go, but almost every nuke that applied for an officer program while I was on the sub got picked up with the exception of a couple dirtbags. If you have a good work ethic and play well with others this probably will not be an issue.
3. As far as working hours go, we were on 18 hour days while underway on the sub. 6 hours of watch, followed by 6 hours maintenance/collateral duties/left over free time, then 6 hours to sleep under ideal circumstances. Free time will all vary with whatever is going on at the moment. On a side note, you will have more free time on a carrier than on a sub, but its a different experience. People on carriers tend to be more specialized and militaristic, while the sub fleet leans more to the jack-of-all-trades mentality, and the crew will be much more close knit.
Good luck in your enlistment. Its going to be tough, but I'm willing to say that if you can succeed here, you will most definetly be able to succeed anywhere.